A NOTE ON THE MULTILINEAR SINGULAR INTEGRAL OPERATORS |
| |
作者单位: | University of Information Engineering,China |
| |
摘 要: | Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 <α≤ 1) and implies the Lp(Rn) (1 < p < oo) boundedness for the operator TA. Some endpoint estimates are also established.
|
关 键 词: | 多线性奇异积分算子 零度均匀 端点估计 光滑条件 BMO |
A note on the multilinear singular integral operators |
| |
Authors: | Jiao Yulan |
| |
Institution: | (1) College of Science, University of Information Engineering, P. O. Box 2201-160, 450001 Zhengzhou, P. R. China |
| |
Abstract: | L
p
(R
n
) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives
of order one in BMO(R
n
). We give a smoothness condition which is fairly weaker than that Ω∈Lip
α(Sn−1) (0<α⪯1) and implies theL
p
(R
n
) (1<p<∞) boundedness for the operator TA. Some endpoint estimates are also established. |
| |
Keywords: | multilinear singular integral operator homogeneous of degree zero smoothness condition SINGULAR INTEGRAL OPERATORS estimates established singular integral operator smoothness condition derivatives integrable the unit sphere moment order homogeneous of degree zero boundedness defined |
本文献已被 CNKI 万方数据 SpringerLink 等数据库收录! |